Self-Dual Configurations in a Generalized Abelian Chern-Simons-Higgs Model with Explicit Breaking of the Lorentz Covariance

Abstract

We have studied the existence of self-dual solitonic solutions in a generalization of the Abelian Chern-Simons-Higgs model. Such a generalization introduces two different nonnegative functions, ω 1 (| φ |) and ω (| φ |), which split the kinetic term of the Higgs field, | D μ φ | 2 → ω 1 (| φ |) | D 0 φ | 2 - ω (| φ |) | D k φ | 2, breaking explicitly the Lorentz covariance. We have shown that a clean implementation of the Bogomolnyi procedure only can be implemented whether ω (| φ |) ∝ β | φ | 2 β - 2 with β ≥ 1. The self-dual or Bogomolnyi equations produce an infinity number of soliton solutions by choosing conveniently the generalizing function ω 1 (| φ |) which must be able to provide a finite magnetic field. Also, we have shown that by properly choosing the generalizing functions it is possible to reproduce the Bogomolnyi equations of the Abelian Maxwell-Higgs and Chern-Simons-Higgs models. Finally, some new self-dual | φ | 6 -vortex solutions have been analyzed from both theoretical and numerical point of view.